Vdhs 5-6 steady state handling-rollover

Chapter 5
• Steady State Handling
• Transient Handling
• Suspension Effects On Cornering

Handling
• Ackermann Steering Geometry
• Low Speed Turning
• High Speed Cornering
• Tire Cornering Stiffness
• Cornering equations
• Static Margin
• Suspension effects on Cornering
– Roll Moment Distribution
– Camber Thrust
– Roll Steer
– Lateral Force Compliance Steer
– Aligning Torque
• Effect of Tractive Forces on
Cornering
• Experimental Measurements of
Understeer Gradient
• Transient Response of vehicles
• Roll Over
• Vehicle Dynamic Tests
• Electronic Stability Control

Ackerman Steering Geometry
Fig. 6.1 p. 197 Gillespie

Ackerman Steering Geometry
• Inner front wheel
steer angles
• Outer front wheel steer
angle
• Average Steer angle
Assume small angles!








2
t
R
L
i








2
t
R
L
o
R
L
ave 

Low Speed Turning
• During Low speed Turning Centrifugal forces are
neglected
• Steering is normally effected by changing the heading of
the front wheels
• During turn all tires should be in pure rolling without the
lateral sliding
• To satisfy pure rolling the wheels should follow curved
paths with different radii originating from a common
turn centre

Low Speed Turning
• The terms “Ackerman Steering” or “Ackerman Geometry” are
often used to denote the exact geometry of the front wheels
• The correct angles are dependent on the wheelbase of the
vehicle and the angle of turn
• The other significant aspect of low-speed turning is the off-
tracking that occurs at the rear wheels.
• The off-tracking distance, , may be calculated from simple
geometry relationships as:
R
LR
L
R
L
R
R
L
RR
2
..)
!4!2
1(1cos
2
42

































Low Speed Off tracking
Max Off tracking : 4790 mm

Steady State Handling
• Steady state handling performance is concerned with the
directional behaviour of a vehicle during a turn under
nontime-varying conditions
• Vehicle negotiating a curve with constant radius at a
constant forward speed
• In the steady state handling behaviour the inertia properties
of the vehicle are not involved
• Steady state Handling Simulation Click

High Speed Cornering
• When a vehicle is negotiating a turn at moderate or higher
speeds, the effect of the centrifugal force acting at the centre
of gravity is to be considered
• To balance the centrifugal force, the tires must develop
appropriate cornering forces
• A side force acting on a tire produces a side slip angle
speeds, the four tires will develop appropriate slip angles
• The handling characteristics of the vehicle depend to a great
extent on the relationship between the slip angles of the
front and rear tires.
• Side forces while cornering-Next slide

speeds, the effect of the centrifugal force acting at the centre
of gravity is to be considered
• To balance the centrifugal force, the tires must develop
appropriate cornering forces
Centrifugal Force
mV2/R

• A side force acting on a tire produces a
slip angle
• When a vehicle is negotiating a turn at
moderate or higher speeds, the four
tires will develop appropriate slip
angles
• The handling characteristics of the
vehicle depend to a great extent on the
relationship between the slip angles of
the front and rear tires.
• Simulation of side forces Click

• Cornering Stiffness
)/( radN
F
C
y

 

Factors Affecting Cornering Stiffness
Cornering
coefficient
CC = C/ Fz
Fig: 15.5a, b, c, d & e

)(3.57 rf
R
L
 
Steer Angle required to negotiate a given curve
Cornering Equations
r f

57.3 L/R
r

f

Cornering Equations
R
V
g
W
R
V
L
b
g
W
F
R
V
g
W
R
V
L
c
g
W
F
r
yr
f
yf
22
22














R
V
g
W
CC
F
CF
R
V
g
W
CC
F
CF
r
rr
yr
r
rryr
f
ff
yf
f
ffyf
2
2
1
1












)(3.57 rf
R
L
 
K is a measure of the steady-
state handling behavior.
gRC
VW
gRC
VW
R
L
r
r
f
f


22
3.57 
gR
V
C
W
C
W
R
L
r
r
f
f
2
)(3.57

 
yKa
R
L
 3.57
Where:
K = Understeer gradient(deg/g)
ay = Lateral acceleration(g)

Understeer Gradient
)(
r
r
f
f
C
W
C
W
K


Understeer Gradient due to tire cornering stiffness

Understeer Gradient
• Understeer gradient is a function of the weight distribution and
tire cornering stiffness
• Depending on the value of K, the steady state handling
characteristics can be classified as
– Neutral steer
– Understeer
– Oversteer

Neutral Steer
• The steer angle required to make the turn will be equivalent
to the Ackerman Angle, 57.3 L/R.
• Physically, the neutral steer case corresponds to a balance
on the vehicle such that the “force” of the lateral
acceleration at the CG causes an identical increase in slip
angle at both the front and rear wheels.
• This is a typical situation when cornering speed is low, and
all four tires have more or less the same weight on them.
• No slipping
R
L
C
W
C
W
K rf
r
r
f
f
3.57
;0






Understeer
• On a constant-radius turn, the steer angle will have to increase
with speed in proportion to K (deg/g) times the lateral
acceleration in g’s. Thus it increases linearly with the lateral
acceleration and with the square of the speed.
• In the understeer case, the lateral acceleration at the CG
causes the front wheels to slip sideways to a greater extent
than at the rear wheels.
• Thus to develop the lateral force at the front wheels necessary
to maintain the radius of turn, the front wheels must be steered
to a greater angle.
rf
r
r
f
f
K
C
W
C
W


 ;0;

Understeer
• Front wheels slipping. The car is not turning around the
expected point N
• Instead, it's turning around the intersection point U,
which makes for a larger turning radius than expected.

Oversteer
• On a constant-radius turn, the steer angle will have to
decrease as the speed (and lateral acceleration) is increased.
In this case, the lateral acceleration at the CG causes the slip
angle on the rear wheels to increase more than at the front.
• The outward drift at the rear of the vehicle turns the front
wheels inward, thus diminishing the radius of turn.
• The increase in lateral acceleration that follows causes the
rear to drift out even further and the process continues
unless the steer angle is reduced to maintain the radius of
turn.
rf
r
r
f
f
K
C
W
C
W


 ;0;

Oversteer
• Rear wheels slipping. This leads to a condition called oversteer,
where the turning radius is smaller than expected.
Demo Click

Steer Angle with Speed
• The way in which steer angle changes
with speed on a constant-radius turn
for each of these cases is illustrated in
Fig. With a neutral steer vehicle, the
steer angle to follow the curve at any
speed is simply the Ackerman Angle.
• With understeer the angle increases
with the square of the speed, reaching
twice the initial angle at the
characteristic speed.
• In the oversteer case, the steer angle
decreases with the square of the speed
and becomes zero at the critical speed
value.

Characteristic Speed
• Characteristic speed is simply the speed at which the steer angle
required to negotiate any turn is twice the Ackerman Angle.
KLgV
R
L
gR
V
K
RLKa
KaRLRL
char
y
y
/3.57
3.57
/3.57
/3.57/3.572
2




• For an understeer vehicle, the understeer level may be
quantified by characteristic speed.

Critical Speed
• In an oversteer vehicle, critical speed is the speed above
which the vehicle becomes unstable
KLgV
R
L
gR
V
K
RLKa
KaRL
crit
y
y
/3.57
3.57
/3.57
/3.570
2




• An Oversteer vehicle can be driven at speeds less than the
critical

Comments
• The primary factors controlling the steady state handling
characteristics of a vehicle are the weight distribution of the
vehicle and cornering stiffness of the tires
• A front engined, front wheel drive vehicle with a large
portion of the vehicle weight on the front tires may tend to
exhibit understeer behaviour
• A rear-engined, rear-wheel drive car with a large portion of
the vehicle weight on the rear tires may tend to have
oversteer characteristics
• Changes in the load distribution will alter the handling
behaviour of a vehicle
• It is necessary choose right type of tire to have right
handling characteristics

Steady State Response to Steering Input
• During a turning maneuver, the steer angle induced by the
driver can be considered as input to the system and the motion
variables of the vehicle such as yaw velocity, lateral
acceleration, and curvature may be regarded as outputs.
• The ratio of yaw velocity, lateral acceleration, or curvature to
the steering input can then be used for comparing the response
characteristics of different vehicles
Steering Angle
Yaw Velocity
Lateral Acceleration
Radius of Curvature

Lateral Acceleration Gain
Lg
KV
Lg
V
gR
V
K
R
L
gR
V
Ka
R
L
gR
V
a
y
y
3.57
1
3.57
3.57
3.57
2
2
2
2
2







• Note that when K is zero (neutral
steer), the lateral acceleration gain
is determined only by the numerator
and is directly proportional to speed
squared.
• When K is positive (understeer), the
gain is diminished by the second
term in the denominator, and is
always less than that of a neutral
steer vehicle.
• Finally, when K is negative
(oversteer), the second term in the
denominator subtracts from 1,
increasing the lateral acceleration
gain.
• The ratio of lateral
acceleration, ay, to the
steering angle, . is
the lateral acceleration
gain,

Yaw Velocity Gain
gainvelocityYaw
Lg
KV
LVr
s
R
V
angleheadinginrotationofrateyYawvelocit




3.57
1
/
deg/3.57
2

• In the case of the
understeer vehicle, the yaw
velocity increases with
speed up to the
characteristic speed, then
begins to decrease
thereafter. Thus the
characteristic speed has
significance as the speed at
which the vehicle is most
responsive in yaw.
Yaw Velocity r is the rate of rotation in heading angle and is given by
r=57.3 V/R

Curvature Response
• The ratio of the steady state curvature 1/R to the steer
angle is another parameter commonly used for evaluating
the response characteristics of a vehicle
• From the steering response point of view, the oversteer
vehicle has the most sensitive handling characteristics,
while the understeer vehicle is the least responsive
gKVL
R
/
1/1
2




Side Slip Angle ()
• When the lateral
acceleration is
negligible, the rear wheel
tracks inboard of the
front wheel. But as
lateral acceleration
increases, the rear of the
vehicle must drift
outboard to develop the
necessary slip angles on
the rear tires.
High speed Turning
Low speed Turning

Directional Stability
• The directional stability of a vehicle refers to its ability to
stabilise its direction of motion against disturbances.
• A vehicle is considered to be directionally stable if,
following a disturbance, it returns to a steady state regime
within a finite time
• A directionally unstable vehicle diverges more and more
from the original path, even after the disturbance is
removed
• The disturbances may arise from crosswind, momentary
forces acting on the tires from the road, slight movement of
the steering wheel, and a variety of causes

Condition for Stability
ifK
g
V
L x
0
2

If K is positive (understeer vehicle) the vehicle is always stable
If K is negative, the vehicle will be stable only
K
gL
Vx


Vehicle Velocity must be less than critical velocity

Static Margin
• Static margin like understeer coefficient or characteristic
speed, provides a measure of the steady-state handling
behavior.
• Static margin is determined by the point on the vehicle where a
side force will produce no steady-state yaw velocity (i.e., the
neutral steer point).
• The neutral steer line is the locus of points in the x-z plane
along which external lateral forces produce no steady-state
yaw velocity.

• The static margin is defined as the distance the neutral steer
points falls behind the CG, normalized by the wheelbase. That
is:
Static Margin = e/L
• When the point is behind the CG the static margin is positive
and the vehicle is understeer. At the CG the margin is zero and
the vehicle is neutral steer. When ahead of the CG, the vehicle
is oversteer. On typical vehicles the static margin falls in the
range of 0.05 to 0.07 behind the CG.
Static Margin
Neutral steer line

Suspension Effects On Cornering
• Although tire cornering stiffness was used as the basis
for developing the equations for understeer/oversteer,
there are multiple factors in vehicle design that may
influence the cornering forces developed in the
presence of a lateral acceleration.
• Any design factor that influences the cornering force
developed at a wheel will have a direct effect on
directional response.
• The suspensions and steering system are the primary
sources of these influences

Suspension Effects on Cornering
– Roll Moment Distribution
– Camber Change
– Roll Steer
– Lateral Force Compliance Steer
– Aligning Torque
– Effect of Tractive Forces on Cornering

Roll Moment and Roll Axis
Fig: 16.4
Roll Axis

Body Roll
• When thinking of load transfer it may help to consider body
roll.
• As the body rolls the outside springs are compressed and place
more load on the outside tires.
• In reality, body roll is a result of cornering force, not a cause
of load transfer.
• If you double the spring rate you will NOT significantly
change the load transfer, but you will reduce body roll.

• If the lateral force, we are talking about, happens on the front
wheels, then the vehicle understeers, if happens on the rear
wheels, then the vehicle oversteers
• Roll moment distribution changes vehicle handling
characteristics. If roll moment distribution is high on front
axle, the vehicle understeers, it oversteers if the roll moment
distribution is high on rear axle
• Auxiliary roll stiffners (Stabilising bars) alter handling
characteristics
• Using stabilising bar, the roll moment on the front axle can be
increased, thus making vehicle understeer
• Using stabilising bars at the rear increase the roll moment on
the rear side making the vehicle oversteer

Mechanics of Roll Moment Distribution
• All suspensions are functionally equivalent to the two
springs.
• The lateral separation of the springs causes them to develop
a roll resisting moment proportional to the difference in roll
angle between the body and axle
K : Roll stiffness of the suspension
Ks : Vertical Spring rate of the left and right springs
s:Lateral separation between the springs
; Roll angle of the body

Mechanics of Roll Moment
 ksk
ss
k
ss
kM ssscG 























 2
2
1
2222
ks
ks
s
If a roll bar is included then
2
sφ
2
s0.5ksuspensiontheofstiffnessRollK
)(
2
1

   rrscG kkkskM

Lateral Load Transfer
Assume a vehicle is taking a turn
Fz0 = vertical load on the outside wheel
in turn
Fzi= Vertical load on the inside wheel
in turn
Fy= lateral force= Fyi+Fyo
hr=Roll Centre height
t= Track width
K  =Roll stiffness of the suspension
= Roll angle of the body
To Determine the Load coming on the left and Right Wheels

Taking moment about the Roll Centre
t
K
rollvehicletoduetransferloadLateral
t
hF
forcecorneringtoduetransferloadLateral
t
K
t
h
F
t
K
t
h
FFFF
KhFF
t
FF
ry
r
y
r
yiyziz
ryiyziz








2
2
22
2)(2
0)(
2
)(
00
00






2
5.0 sksuspensiontheofstiffnessRollK s
=Roll Angle
1
1
1
2
1 /
WhKK
aWh
WhKK
RgVWh
rf
y
rf 






equationsforegoingFrom
carspassengertypicalon
greestoofrangetheinusuallyisraterollThe
WhKK
Wh
da
d
RateRoll
rfy
/deg73
1
1





Roll Rate

Roll Moment
rzrrr
rf
rr
fzfff
rf
ff
tF
Rg
V
hW
WhKK
RgVWh
KM
tF
Rg
V
hW
WhKK
RgVWh
KM
MomentsRoll






2
1
2
1'
2
1
2
1'
)/(
)/(




The Roll moments magnitude depend on Kf and K t which
in turn depend on suspension stiffness

Lateral Forces Fyf and Fyr
gR
VW
FbCF
tiresreartheon
gR
VW
FbCF
r
rzryr
f
fzfyf
2
2
2
2
]2[
]2[






b is the second coefficient in the cornering stiffness polynomial










]2[
]2[
]2[
]2[
2
2
2
2
2
2
2
2
zr
r
r
r
rzryr
zf
f
f
f
fzfyf
FbCgR
VW
gR
VW
FbCF
FbCgR
VW
gR
VW
FbCF






Slip Angles due to Lateral Force

r
zr
r
r
f
zf
f
f
llt
r
zr
r
r
f
zf
f
f
r
r
f
f
z
zz
z
zrrzff
f
rf
C
Fb
C
W
C
Fb
C
W
K
gR
V
C
Fb
C
W
C
Fb
C
W
C
W
C
W
R
L
C
Fb
C
C
Fb
C
FbC
FbC
FbC
RgWrV
FbC
RgVW
R
L
R
L











22
222
2
22
2
2
2
2
2
22
)]
22
()[(3.57
)
2
1(
1
)
2
1(
1
)2(
1
2
)2(
/
)2(
/
3.57
)(3.57




















Understeer Gradient Due to Roll Moment Distribution

Understeer Gradient
r
zr
r
r
f
zf
f
f
llt
f
zf
f
f
r
r
f
f
C
Fb
C
W
C
Fb
C
W
K
C
W
C
Fb
C
W
C
W
C
W
R
L
C





22
2
22
2
()[(3.57







Understeer Gradient due
to lateral load transfer
It is the understeer gradient that arises due to lateral load transfer

In general, the roll moment distribution on vehicles tends to be
biased toward the front wheels due to a number of factors:
• Relative to load, the front spring rate is usually slightly lower
than that at the rear (for flat ride), which produces a bias
toward higher roll stiffness at the rear. However, independent
front suspensions used on virtually all cars enhance front roll
stiffness because of the effectively greater spread on the front
suspension springs (increased s, but less ks).
• Designers usually strive for higher front roll stiffness to ensure
under-steer in the limit of cornering.
• Stabilizer bars are often used on the front axle to obtain higher
front roll stiffness.
• If stabilizer bars are needed to reduce body lean, they may be
installed on the front or the front and rear. Caution should be
used when adding a stabilizer bar only to the rear because of
the potential to induce unwanted oversteer.

Camber Change
• The inclination of a wheel outward from the body is known as
the camber angle. Camber on a wheel will produce a lateral
force known as “camber thrust.” Fig: shows a typical camber
thrust curve.

• Camber angle produces much less lateral force than slip
angle. About 4 to 6 degrees of camber are required to
produce the same lateral force as 1 degree of slip angle on a
bias-ply tire.
• Camber stiffness of radial tires is generally lower than that
for bias-ply tires; hence, as much as 10 to 15 degrees are
required on a radial. Nevertheless, camber thrust is additive
to the cornering force from slip angle, thus affecting
understeer gradient.
• Camber thrust of bias-ply tires is strongly affected by
inflation pressure, although not so for radial tires, and it is
relatively insensitive to load and speed for both radial and
bias tires.
Camber Change

Camber Change
• Camber angles are small on solid axles, and at best only change
the lateral forces by 10% or less. On independent wheel
suspensions, however, camber can play an important role in
cornering.
• Camber changes both as a result of body roll and the normal
camber change in jounce/rebound.
• The understeer gradient deriving from camber angles on each axle
is given by:
y
r
r
rf
f
f
camber
aC
C
C
C
K

















)(


yF
StiffnessCamberTireC 

Roll Steer
• When a vehicle rolls in cornering, the suspension kinematics
may be such that the wheels steer. Roll steer is defined as the
steering motion of the front or rear wheels with respect to the
sprung mass that is due to the rolling motion of the sprung
mass. Consequently, roll steer effects on handling lag the steer
input, awaiting roll of the sprung mass.
• The steer angle directly affects handling as it alters the angle
of the wheels with respect to the direction of travel. Let “” be
the roll steer coefficient on an axle (degrees steer/degree
roll).
• The understeer gradient resulting due to roll steer
y
rfsteerroll
a
K




 )(

• Positive roll steer on the rear axle oversteers the vehicle
• Positive roll steer on the front axle understeers the vehicle
Compression of suspension arm,
hence pushes the frame forward
Taking a turn

Lateral Force Compliance Steer
• With the soft bushings used in suspension linkages for NVH
reasons, there is the possibility of steer arising from lateral
compliance in the suspension.
• With the simple solid axle, compliance steer can be
represented as rotation about a yaw center as illustrated in

• With a forward yaw center on a rear axle, the compliance
allows the axle to steer toward the outside of the turn, thus
causing oversteer. Conversely, a rearward yaw center results
in understeer
• On a front axle, just the opposite is true - a rearward yaw
center is oversteer, and a forward yaw center is understeer
• The lateral force understeer gradient is given by
Klfcs= AfWf-ArWr
• A=Lateral force compliance=/Fy

Aligning Torque
• When a side force applied at the wheel centre and the
cornering force developed in the ground plane are
usually not coplanar. At some slip angle, the cornering
force in the ground plane is normally behind the applied
side force giving rise to a torque called aligning torque.
The distance is known as the “pneumatic trail (p).”
• The aligning torque experienced by the tires on a
vehicle always resists the attempted turn, thus it is the
source of an understeer effect.

Positive
Caster point
Aligning Moment
Tyre Slip Angle
rf
rf
at
CC
CC
L
p
WK

 


• Because the C values are positive, the aligning torque
effect is positive (understeer) and cannot ever be negative
(oversteer).
• The understeer due to this mechanism is normally less than
0.5 deg/g. However, aligning torque is indirectly
responsible for additional, and more significant, understeer
mechanisms through its influence on the steering system.

Effect of Tractive Forces on Cornering
• Considering tractive forces , the Understeer gradient equation
can be written as follows:
)(
r
xr
r
r
f
xf
f
f
tf
C
F
C
W
C
F
C
W
K


Fig: 16.10

• If Fxf is positive it causes an oversteer influence (pulls
the front of the vehicle into the turn). Thus this
mechanism is an oversteer influence with a FWD in the
throttle-on case.
• If Fxr is positive it causes an understeer influence by the
same reasoning on a RWD.
• On a 4WD these mechanisms would suggest that the rear
axle should “over drive” the front axle to ensure
understeer behavior.

FWD Understeer Influences
• But in most cases, throttle-on produces understeer, and throttle-
off produces oversteer
)(
r
xr
r
r
f
xf
f
f
tf
C
F
C
W
C
F
C
W
K


• In a front wheel drive vehicle, as per the equation derived the
vehicle oversteers

FWD Understeer Influences
• The primary mechanisms responsible for throttle on/off
changes in understeer of a FWD vehicle are:
– The lateral component of drive thrust – While this mechanism is
relatively weak (<0.5 deg/g), it is oversteer in direction.
– Drive torque acting about the steer axis – Highly dependent on
driveline geometry and the degree of body roll in cornering, this
mechanism is understeer in direction (about 1 deg/g).
– Loss of lateral force – A tire property which causes understeer (about 1
– 1.5 deg/g).
– Increase in aligning moment – A tire property which causes under-steer
(about 0.5-1 deg/g).
– Fore/aft load transfer – Although present on FWD and RWD vehicle, it
is always understeer in direction (about 1 deg/g).

SUMMARY OF UNDERSTEER EFFECTS
• The understeer coefficient, K, for a vehicle is the result of
tire,vehicle and steering system parameters. Its total value is
computed as the sum of a number of effects as summarized in the
following table.
UNDERSTEER COMPONENT SOURCE
r
r
f
f
tiffnescornerings
C
W
C
W
K


y
r
r
rf
f
f
camber
aC
C
C
C
K









)(





Tire cornering stiffness
Camber thrust
yrfsteerroll aK  /)(  Roll steer
r
zr
r
r
f
zf
f
f
llt
C
Fb
C
W
C
Fb
C
W
K

22
22 


 Lateral load transfer

rrfflf WAWAK CS

rf
rf
at
CC
CC
l
p
WK

 

ss
fstrg
K
pr
WK



UNDERSTEER COMPONENT SOURCE
Lateral force compliance steer
Aligning torque
Steering system
)(
r
xr
r
r
f
xf
f
f
tf
C
F
C
W
C
F
C
W
K

 Tractive Forces
= caster angle, Kss –Steering System stiffness

How much Understeer Gradient
K- Understeer Gradient value is dependent on Steering ratio desired for
different class of vehicles

Testing of Handling Characteristics
• To test handling under steady state conditions, various types of
tests can be conducted on a skid pad, which in essence is a large,
flat, paved area.
• Three types of tests can be distinguished
– Constant radius test
– Constant forward speed test
– Constant steer angle test
• During the tests, the steer angle, forward speed and yaw velocity
or lateral acceleration of the vehicle are measured
• Yaw velocity measured by a rate gyro or lateral
acceleration/forward speed
• Lateral acceleration can be measured by an accelerometer or yaw
velocity x forward speed
• Based on the relationship between the steer angle and lateral
acceleration or yaw velocity obtained handling characteristics can
be evaluated

Constant Radius Test
• Vehicle is driven along a
constant radius at various speeds
• The steer angle required to
maintain the vehicle on course at
various forward speeds together
with the corresponding lateral
acceleration are measured
• Results are plotted
• The handling behaviour of the
vehicle can then be determined
from the slope of steer angle-
lateral acceleration curve
Fig: 15.20

Constant Speed Test
• The vehicle is driven at a
constant forward speed at
various turning radii.
• The steer angle and the lateral
acceleration are measured
• The handling behaviour of the
vehicle can then be determined
from the slope of the steer
angle-lateral acceleration curve
• The vehicle is understeer when
the slope is greater than that of
neutral steer slope, vehicle is
oversteer when the slope is less
than neutral steer curve slope
Fig: 15.21

Constant Steer Angle Test
• The vehicle is driven with a fixed
steering wheel angle at various
forward speeds.
• Curvature Vs lateral acceleration
curve is drawn and the handling
characteristic is determined
• The constant radius test is
simplest and requires little
instrumentation, constant speed
test is more representative of the
actual road behaviour of a vehicle
than the constant radius test as the
driver usually maintains a more or
less constant speed in a turn and
turns the steering wheel by the
required amount to negotiate the
curve. The constant steer angle
test is easy to execute.
Fig: 15.22

Transient Response Characteristic
• Vehicle will be in a transient state between the application of
steering input and the attainment of steady state motion
• The behaviour of the vehicle in this period is usually referred
to as transient response characteristics
• The overall handling quality of a vehicle depends to a great
extent on its transient behaviour
• The optimum transient response of a vehicle is that which
has the fastest response with a minimum of oscillation in the
process of approaching the steady state motion

Transient Response Characteristic
• While analysing for transient response, the inertia properties of
the vehicle must be taken into consideration
• To describe its motion, it is convenient to use a set of axes
fixed to and moving with the vehicle body because with
respect to these axes, the mass moment of inertia of the vehicle
are constant, where as with respect to axes fixed to earth, the
mass moments of inertia vary as the vehicle changes its
position

Formulation of Transient Motion Equations



.
.
.
,
,22
/
/
.
0
0


















 












bC
CV
geometryandstiffnesscorneringV
ofdependentmatrix
dtd
dtdV
I
m
f
fy
x
y

ADAMS Simulations
• Transient Inputs
– Step steer
– Ramp Steer
– Sinusoidal input

Ramp steer Simulation
Fig: 15.26

Input (sinusoidal steer input)

Vehicle Dynamic Tests
• The intent of these test procedure is to subjectively determine
the road holding ability and handling characteristics of a
vehicle.

High Speed Oval Elk Test
U-Turn Test Circular Test Slalom Test

Test Purpose
High Speed Oval Wheel Motion Data Recording
Elk Test (Double
Lane Change)
Vehicle Handling during fast lane change
U-Turn Body Roll, Roll steer, Lateral Compliance
Circular Skid Test To test understeer and oversteer
Slalom Test Vehicle Dynamic Analysis, Wheel
Packaging Calculations-like camber change

Chapter 6
Roll Over
 Introduction to rollover
 Causes of rollover
 Avoidance of rollover
 Roll over demonstrations
 Simulation-Demonstration (plots/animations etc)

Introduction
• Rollover is a type of vehicle accident, where a vehicle
turns over on its side or roof
• The vehicle rotates 90 degrees or more about its
longitudinal axis (x-axis) such that the body makes contact
with the ground

Introduction
• It may occurs on flat and level surfaces when the lateral
accelerations on a vehicle reach a level beyond that which
can be compensated by lateral weight shift on the tires

Introduction
• Cross-slope of the road (or off-road) surface may
contribute along with disturbance to the lateral forces
arising from curb impacts, soft ground or other
obstructions that may “trip” the vehicle

22%
42%
4%
1%
31%
63%
25%
1%
9%
2%
41%
40%
4%
14%
1%
43%
39%
2%
14%
2%
Cars SUVs
Vans Pickups
Roll Over Fatalities in Different Types of
Vehicles

Roll Over Models-First Order
Track Width-t
Height of CG -h
SSF= Static Stability Factor= t/2h
(Quasi-Static Roll)

0%
10%
20%
30%
40%
50%
1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6
Static Stability Factor
ProbabilityofRolloverperSingleVehicleCrash
Rollover Probability V/S Static Stability
Factor
Reduced Roll Over Tendency

Roll Over-Transient Maneuvers
It can happen during Step Steer

Tripping
• NHTSA data show that 95% of single-vehicle rollovers are
tripped
• This happens when a vehicle leaves the roadway and slides
sideways, digging its tires into soft soil or striking an object
such as a curb or guardrail
• The high tripping force applied to the tires in these
situations can cause the vehicle to roll over

Causes of Rollover
• Increased height of CG will increase the tendency to
roll over
• The vehicle can overturn when it strikes a ditch or
embankment, or is tripped by soft soil
• High Lateral forces cause vehicle Roll over
Active Safety System
Incorporating active safety systems like ESC (Electronic
stability Control ) can reduce the chances of rollover

Avoidance of Roll Over
Tire Pressure
1. Improperly inflated and worn tires can be especially
dangerous because they inhibit the ability to maintain
vehicle control
2. Worn tires may cause the vehicle to slide sideways on
wet or slippery pavement, sliding the vehicle off the road
and increasing its risk of rolling over
Loading the vehicle
1. If the vehicle is overloaded and the load distribution is
improper, it increases the tendency to rollover
2. Roof rack should be fitted by considering weight limits
3. Any load placed on the roof will be above the vehicle’s
centre of gravity, and will increase the vehicle’s likelihood of
rolling over

Vehicle Type
• All types of vehicles can rollover. However, taller, narrower
vehicles such as SUVs, pickups, and vans have higher
centres of gravity, and thus are more susceptible to rollover
if involved in a single-vehicle crash
Panic-like Steering
• Many rollovers occur when drivers overcorrect their steering as
a panic reaction to an emergency—or even to a wheel going off
the pavement’s edge
• At highway speeds, overcorrecting or excessive steering can
cause the driver to lose control which can force the vehicle to
slide sideways and roll over
Aerodynamics
• Improper pressure distribution may give rise to side forces

Testing For Rollover
NHTSA Fish Hook Test

What is Vehicle Stability
• Vehicle instability is characterized by Skid, Slide or Spin
(yaw)
• Yaw is rotation around the vertical axis; i.e. spinning left or
right.
• Skidding, Sliding and Spinning of vehicle may happen due
to panic braking, high speed cornering, loss of traction and
due to dynamic (transient) maneuvering
• Vehicle stability control systems must help drivers maintain
control when a vehicle starts to skid, slide or spin
Skidding demo – wheel locking
Sliding Demo – steering (Over Steering)
Spinning demo –Next Slide- loss of traction

Electronic Stability Control
• Electronic Stability control (ESC) is a technology that
improves the safety of a vehicle's handling by detecting and
preventing skids
• When ESC detects loss of steering control, ESC automatically
applies individual brakes to help "steer" the vehicle where the
driver wants to go.
• Braking is automatically applied to individual wheels, such as
the outer front wheel to counter oversteer, or the inner rear
wheel to counter understeer.
• Some ESC systems also reduce engine power until control is
regained

Electronic Stability Control (ESC)
• Electronic Stability Control (ESC) is the generic term for
systems designed to improve a vehicle's handling, particularly at
the limits where the driver might lose control of the vehicle
• Other nomenclatures
– Vehicle Dynamics Control (VDC)
– Electronic Stability Program (ESP)
– Vehicle Stability Assist(VSA)
– Advanced Stability Control (ASTC)
– Direct yaw moment control (DYC)

Braking Control Under Cornering

1. Yaw-rate sensor with
lateral-acceleration
sensor
2. Steering-wheel-angle
sensor
3. Primary-pressure
sensor
4. Wheel-speed sensor
5. ESP control unit
6. Hydraulic modulator
7. Wheel brakes
8. Engine management
9. Fuel injection – only
for gasoline engine:
10. Ignition-timing
intervention
11. Throttle-valve
intervention (ETC)
ESP – Control Loop
Fig: 8.6

Vdhs 5-6 steady state handling-rollover

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